Description Usage Arguments Details Value Methods (by class) See Also Examples
The oc1S
function defines a 1 sample design (prior, sample
size, decision function) for the calculation of the frequency at
which the decision is evaluated to 1 conditional on assuming
known parameters. A function is returned which performs the actual
operating characteristics calculations.
1 2 3 4 5 6 7 8 9 10 
prior 
Prior for analysis. 
n 
Sample size for the experiment. 
decision 
Onesample decision function to use; see 
... 
Optional arguments. 
sigma 
The fixed reference scale. If left unspecified, the default reference scale of the prior is assumed. 
eps 
Support of random variables are determined as the
interval covering 
The oc1S
function defines a 1 sample design and
returns a function which calculates its operating
characteristics. This is the frequency with which the decision
function is evaluated to 1 under the assumption of a given true
distribution of the data defined by a known parameter
θ. The 1 sample design is defined by the prior, the
sample size and the decision function, D(y). These uniquely
define the decision boundary, see
decision1S_boundary
.
When calling the oc1S
function, then internally the critical
value y_c (using decision1S_boundary
) is
calculated and a function is returns which can be used to
calculated the desired frequency which is evaluated as
F(y_cθ).
Returns a function with one argument theta
which
calculates the frequency at which the decision function is
evaluated to 1 for the defined 1 sample design. Note that the
returned function takes vectors arguments.
betaMix
: Applies for binomial model with a mixture
beta prior. The calculations use exact expressions.
normMix
: Applies for the normal model with known
standard deviation σ and a normal mixture prior for the
mean. As a consequence from the assumption of a known standard
deviation, the calculation discards sampling uncertainty of the
second moment. The function oc1S
has an extra
argument eps
(defaults to 10^{6}). The critical value
y_c is searched in the region of probability mass
1eps
for y.
gammaMix
: Applies for the Poisson model with a gamma
mixture prior for the rate parameter. The function
oc1S
takes an extra argument eps
(defaults to 10^{6})
which determines the region of probability mass 1eps
where
the boundary is searched for y.
Other design1S:
decision1S_boundary()
,
decision1S()
,
pos1S()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53  # noninferiority example using normal approximation of loghazard
# ratio, see ?decision1S for all details
s < 2
flat_prior < mixnorm(c(1,0,100), sigma=s)
nL < 233
theta_ni < 0.4
theta_a < 0
alpha < 0.05
beta < 0.2
za < qnorm(1alpha)
zb < qnorm(1beta)
n1 < round( (s * (za + zb)/(theta_ni  theta_a))^2 )
theta_c < theta_ni  za * s / sqrt(n1)
# standard NI design
decA < decision1S(1  alpha, theta_ni, lower.tail=TRUE)
# double criterion design
# statistical significance (like NI design)
dec1 < decision1S(1alpha, theta_ni, lower.tail=TRUE)
# require mean to be at least as good as theta_c
dec2 < decision1S(0.5, theta_c, lower.tail=TRUE)
# combination
decComb < decision1S(c(1alpha, 0.5), c(theta_ni, theta_c), lower.tail=TRUE)
theta_eval < c(theta_a, theta_c, theta_ni)
# evaluate different designs at two sample sizes
designA_n1 < oc1S(flat_prior, n1, decA)
designA_nL < oc1S(flat_prior, nL, decA)
designC_n1 < oc1S(flat_prior, n1, decComb)
designC_nL < oc1S(flat_prior, nL, decComb)
# evaluate designs at the key logHR of positive treatment (HR<1),
# the indecision point and the NI margin
designA_n1(theta_eval)
designA_nL(theta_eval)
designC_n1(theta_eval)
designC_nL(theta_eval)
# to understand further the dual criterion design it is useful to
# evaluate the criterions separatley:
# statistical significance criterion to warrant NI...
designC1_nL < oc1S(flat_prior, nL, dec1)
# ... or the clinically determined indifference point
designC2_nL < oc1S(flat_prior, nL, dec2)
designC1_nL(theta_eval)
designC2_nL(theta_eval)
# see also ?decision1S_boundary to see which of the two criterions
# will drive the decision

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